On the distribution and moments of the strength of a bundle of filaments

Abstract

SummarySmall sample and large sample properties of the bundle strength of parallel filaments studied earlier by Daniels (1945) and Sen, Bhattacharyya, Suh (1969) have been developed here by probabilistic argument. The statistics belong to a family or class of statistics, each of which forms a reverse semi-martingale sequence. Certain moment properties are also discussed.

Lower tail analysis of the distribution of the strength of load-sharing systems

“…Proof. The proof is a straightforward extension of the method of Suh, Bhattacharyya, and Grandage (1970) for equal load sharing. Let E. for i in S denote the event that fiber i has strength at most XA i (S) and the system S fails under load x.…”

“…which is equivalent to Equation (2.6) of Suh et al (1970) rewritten in terms of load per fiber instead of total load. The formula is originally due to Daniels (1945).…”

Tensile Behavior of Slack Fiber Bundles—Theory and Application to HVI Testing

“…In a well combed and brush~d fiber bundle, assumptions 1 and 2 should hold; assumption 3 is widely accepted for cotton fibers; assumption 4 on the independence of fiber tensile properties is essential for simplifying model development; and assumption 5 is made because small bundle properties are quite complex and nonlinear with respect to the number of fibers in the bundle, whereas they quickly approach asymptotic limits as the bundle size becomes sufficiently large [ 19]. These assumptions provide much simplification for studying a large fiber bundle and its tensile behavior.…”

“…Theoretical studies on the tensile behavior of straight fiber bundles can also be found in papers by Daniel [?., 3], Platt~ 15). Coleman 111, Suh [ 18,19], Phoenix [10][11][12][13], Duckett 141. and Pitt [ 14]. Extensive experimental work on straight fiber bundles has been reported by several researchers 17, 15,16,23].…”

Evaluating Single Fiber and Fiber Bundle Tensile Curves

“…Theoretical studies on the tensile behavior of ideal (straight) fiber bundles were also completed by Daniels [5], Coleman [3], Suh et al [28], Duckett [91, Phoenix . I , 876 [ 19,22], and Pitt [23].…”